Question: Simplify the following expression: $\dfrac{8t^3}{4t^4}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{8t^3}{4t^4} = \dfrac{8}{4} \cdot \dfrac{t^3}{t^4} $ To simplify $\frac{8}{4}$ , find the greatest common factor (GCD) of $8$ and $4$ $8 = 2 \cdot 2 \cdot 2$ $4 = 2 \cdot 2$ $ \mbox{GCD}(8, 4) = 2 \cdot 2 = 4 $ $ \dfrac{8}{4} \cdot \dfrac{t^3}{t^4} = \dfrac{4 \cdot 2}{4 \cdot 1} \cdot \dfrac{t^3}{t^4} $ $\phantom{ \dfrac{8}{4} \cdot \dfrac{3}{4}} = 2 \cdot \dfrac{t^3}{t^4} $ $ \dfrac{t^3}{t^4} = \dfrac{t \cdot t \cdot t}{t \cdot t \cdot t \cdot t} = \dfrac{1}{t} $ $ 2 \cdot \dfrac{1}{t} = \dfrac{2}{t} $